There are calls for level 4 rule changes so teachers can visit disabled children in their homes.
School principals say some children with special education and behaviour needs do not cope well with remote learning.
They say the children and their families need more support than they can get over the internet.
Pukekohe woman Kristen Hughes said she was in lockdown with her husband Jeff, daughter Hannah and 17-year-old son Liam, who has autism.
She said trying to get Liam to accept that he should learn at home could be more trouble than it was worth.
"School happens at school, it's not something that happens at home so it's very hard to get that point across to him so Jeff and I and his sister as teachers fail miserably," she said.
Hughes said her son loved his school's online music and exercise sessions but he would really benefit from home visits.
"Having somebody come in, even if it was only for half-an-hour, 45 minutes a day or every second day just so that there was some continuity for contact and so they know that they haven't been abandoned," she said.
The principal of Berhampore School in Wellington, Mark Potter, said remote learning could be tricky for some children with special needs.
"For families with children with disabilities that have additional learning needs, it's very difficult learning from home. Many of those children use their adults that they have at school as part of their learning process, they don't necessarily respond so well to screens and they find it very difficult without having someone there helping them facilitate and navigate their learning."
He said lockdown was putting a lot of pressure on some families.
The government had made an exemption to level 4 rules enabling childcare for the children of essential workers and it should also make an exemption allowing support for disabled children.
"If we had the capacity to have specialist staff that a lot of schools do have, who can actually provide support while maintaining limited safe bubbles, that would be very helpful," he said.
"There are some organisations that are approved home-carers but they have no relationship with the child or the family and that makes it really tough."
The principal of Parkside Specialist School in Pukekohe, Carol Willard, said the school was tailoring its remote learning to the needs of each child and it also provided group music and exercise sessions.
She said during lockdowns families were trying to do work that schools did with groups of teachers, specialists and aides.
"The families are kind of just left to cope with it on their own. And that's what we found, it's very, very difficult for our families to access support that they might need once they're in lockdown.
"And that isn't just with the students, the children they're dealing with, it's things like getting out to get essential provisions and medications and whatever as well," he said.
Willard said society should be thinking about the needs of disabled children first and foremost.
"Rather than an afterthought or not a thought at all, which seems to be the case sometimes, we should be thinking first about our most vulnerable students in the country because if we're thinking of those students and the needs of them and their families, we can look after everybody," she said.
Education Ministry deputy secretary sector enablement and support Helen Hurst said schools could get help with remote learning for children with special needs from resource teachers of learning and behaviour and from the ministry's specialists.
"For instance, our specialists are doing 'home visits' and assessments by Skype, using videos to complete observations, carrying out 'telepractice' sessions over the phone, and helping families to use what they have available in their homes to support the learning of their young people," she said.
Special Education Principals Association president Sally Wilkinson said she did not believe teachers should visit special needs children in their homes.
She said pastoral care for children and their families was important, and schools were providing that support through video-conferencing and phone calls.
Wilkinson said specialist schools should remain shut even if the alert level changed to level three because many of their students had difficulty wearning masks and needed help with personal hygiene and feeding.
She said last year some schools remained closed at level three, but others were compelled to open.